The relation between time t and displacement x is `t = alpha x^2 + beta x,` where `alpha and beta` are constants. The retardation is

Options

A. `2 alpha v^3`
B. `2 beta v^3`
C. `2 alpha beta v^3 `
D. `2 beta^2 v^3`

Answer

A

Explanation

`t = alpha x^2 + beta x`
`rArr 1 = 2alpha xx (dx)/(dt) + beta (dx)/(dt)`
`(dx)/(dt) =v = (1)/(2 alpha x + beta)`
Now, `a = (dv)/(dt) = (dv)/(dx) . (dx)/(dt)`
` = ([2alpha + beta).0 -1 xx 2alpha])/((2alpha x + beta)^2) . (1)/((2alpha x + beta))`
`a = (-2alpha)/((2alpha x+ beta)^3) = -2alpha v^3` [ here -sign indicates retardation]